Q13 of 140 Page 267

Prove that (n + 2) × (n!) + (n + 1) ! = (n!). (2n + 3)

To Prove :


Formula :


L.H.S. = (n + 2) × (n!) + (n + 1)!


= (n + 2) × (n!) + (n + 1) × (n!)


= (n!) × [(n + 2) + (n + 1)]


= (n!) × (2n + 3)


= R.H.S.


∴L.H.S. = R.H.S.


Conclusion : (n + 2) × (n!) + (n + 1)! = (n!) × (2n + 3)


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